The goals are (1) to develop a general nonlinear blood-tissue exchange model that can allow investigators to explore with great flexibility the possible kinetics over a range of studies; (2) to have a general model that serves as a design and testing tool for further design of either simplified models tailored for specific applications or more complex models such as a whole body re-circulatory, regulatory model; and (3) to develop a accurate, robust and efficient numeric scheme for solving nonlinear kinetic problems. In order to achieve these goals, we have greatly expanded MMID4 and MSID4, two previously developed blood-tissue exchanged models, to incorporate a number of nonlinear features that describe the commonly encountered biochemical events, such as substrate binding, Michaelis-Menten kinetics, carrier-mediated transmembrane transport, and biunireactant kinetics. This model can be easily tailored for specific tracer kinetic studies, such as beta-receptor ligand binding in the heart, cardiac purine metabolism, and pre-synaptic cardiac sympathetic function. This model also allows time-varying model parameters that can be used to design feed-back regulatory models. In order to numerically handle these nonlinear biochemical events, two classes of advanced ODE solvers for nonlinear stiff problems have been added: (1) a variant of back differentiation formulae, and (2) a variant of implicit Runge-Kutta method. This model has been implemented under XSIM and is being used by our collaborators as well as being used for our workshop for kinetic modeling.